Intrinsic and extrinsic geometric properties of string world sheets in a curved space-time background are explored. In our formulation, the only dynamical degrees of freedom of the string are its immersion coordinates. A classical equation of motion and the space-time energy-momentum tensor of the string are obtained. One-loop divergent terms are calculated using the background field method. A divergent Euler characteristic term appears in this order. The condition for one-loop finiteness is derived. The results obtained here differ from those in the standard procedure.

• Received 15 April 1996

DOI:https://doi.org/10.1103/PhysRevD.55.3800